Radial Heat Transfer Research Articles

AGENT-TH scheme: New thermal hydraulics (TH) code coupled with the AGENT neutronics code for light water reactors modeling and analysis

In this paper a newly developed thermal hydraulics (TH) code coupled with the state-of-the-art neutronics deterministic code AGENT (Arbitrary Geometry Neutron Transport) is presented. This coupled system is called the AGENT-TH scheme. The neutronics AGENT code uniquely combines the method of characteristics (MOC) and R-function geometrical modeling to solve the 2D/3D neutron transport in nuclear reactors of current or future designs. Commonly, the cross sections are prepared using the SCALE code system. The implementation of the TH code with AGENT enables coupled thermal-hydraulic and neutronics analysis in providing the average reactor fuel temperatures. This allows for an accurate overall power profiling within the reactor system, which affects reactor coolant temperature, neutron flux, and other associated reactor parameters.The two main types of LWRs are boiling water reactors (BWRs) and pressurized water reactors (PWRs). The BWRs operate at lower pressures than PWRs, which results in a higher void fraction, or fraction of coolant flow which is vapor versus liquid. Performances of PWRs, with a higher operating pressure, may be obtained using the homogeneous equilibrium mixture (HEM) model, which assumes a slip relation equal to one between the coolant liquid and vapor phases. To account for the higher void fraction in the BWR coolant, the BWRs properties are assessed based on the drift flux model. The thermal hydraulics drift flux model is developed as a part of the TH code, to address the two-phase flow associated with two-phase heat transfer (including subcooled nucleation and saturated boiling) as found in BWR systems. This is accomplished based on the drift flux equations in 1D steady-state conditions, which permits fast computation times without sacrificing final accuracy.The TH code is benchmarked against the reactor simulation code TRACE for a single pin to assess the thermal-hydraulics capabilities of the drift flux model for the fluid void fraction, flow quality, pressure, saturation temperature, and mixture temperature along the axial height of the pin. The drift flux thermal hydraulics module is coupled with AGENT using a radial heat transfer model taking into account heat transfer from the fuel centerline to the bulk fluid. Fuel temperatures calculated in the TH code are used to update cross sections from the SCALE code system to account for thermal feedback. Reasonable agreements are obtained between the AGENT-TH and TRACE for the presented benchmark examples.

Design, analysis, and implementation of extra low air-gap single-phase axial-flux induction motors for low-cost applications

Summary In this paper, design and prototyping of two-speed capacitor-run single-phase axial-flux induction motor (AFIM) for direct-drive applications is presented. The proposed structure has single stator-single rotor configuration with high magnetic pull between the stator and rotor, which may compel rotor to lock. Although the most efficient method to overcome this problem is using a second rotor or stator in the mirror with the first one, it is not applicable in low-cost applications. So, in this paper, two new and fast construction techniques are proposed to fabricate an AFIM with extra low air-gap length and minimum cost. Beside design and optimization process, a thermal equivalent circuit considering radial and lateral heat transfers is proposed. Then different losses and thermal resistances are exactly calculated to estimate the temperature rise of different motor parts and the maximum specific magnetic and electric loadings. Then, motor performance is evaluated using three-dimensional time-stepping finite-element analysis. Finally, a comprehensive fabrication algorithm for AFIMs is presented, and a prototype of the studied motor is fabricated and tested. The experimental results validate the design, optimization, thermal model, and finite element simulations. Copyright © 2016 John Wiley & Sons, Ltd.

Heat transfer performance of structured catalytic reactors packed with metal foam supports: Influence of wall coupling

Based on previous lab-scale heat transfer experiments performed in a test tube filled with metallic foams, extensive simulations of conjugated heat transfer were performed to systematically investigate the role of different coupling scenarios between the foam structure and the tube wall, using a 3D scanned foam geometry to enable the comparison of simulation results with experiments. The goal of this analysis is to gain insight into the prominent role of the wall coupling for radial heat transfer in a structured catalytic reactor packed with metal foams as catalyst supports. In the current numerical investigation the focus is on the characterization of the contact area between the foam and the reactor wall. Starting from perfect contact between the two, the contact area was decreased by selecting randomly some boundary spots of the foam and considering them as adiabatic. Moreover, the local distribution of the adiabatic struts was restricted to regions near the reactor inlet to additionally investigate the influence of the local distribution of the adiabatic struts at same overall contact areas. Eventually, all the contacts between the foam and the reactor wall were considered adiabatic as the other limiting case, wherein heat transfer at the foam/wall interface was governed solely by convection. The numerical analysis revealed that even if only a limited fraction of the struts have a direct contact with the tube wall, the heat transfer rate is significantly enhanced in comparison to the adiabatic case. In analogy with the previous experimental study, the numerical investigation was carried out for two different gases, nitrogen and helium, in order to address the influence of the thermal conductivity of the fluid phase. For further experimental verification, additional heat transfer measurements were performed for the case of a foam directly sintered to the tube in order to realize a perfect contact between foam and wall.

Handling contact points in reactive CFD simulations of heterogeneous catalytic fixed bed reactors

The mesh generation is a crucial step for Computational Fluid Dynamic (CFD) simulations and incorrect numerical descriptions of the geometry may strongly affect the reliability and the accuracy of the results. This is especially true in handling the contact points in random packed bed of spheres. In this respect, we provide a systematic investigation of the treatment of the contact points for reactive CFD simulations of gas–solid packed beds of spheres. In particular, building on previous literature results on radial heat transfer and pressure drop simulations, we extend and assess the bridge method to reaction at surfaces. At this scope, we first analyze a regular bed of spheres in laminar conditions (Re~80). This regular packed bed and the laminar flow regime allow for a direct and feasible meshing of the contact points, thus giving the possibility to perform explicit comparisons between meshes with and without bridges. In doing so, we identify guidelines that are then extended and tested to the meshing of a random packed bed reactor. In this way, we identify a meshing protocol, which can be adopted to properly describe surface reactivity in packed bed reactors along with a concomitant sound description of pressure drops and heat transfer.

Analytical Study on the Effective Thermal Conductivity of VHTR Fuel Block Geometry with Multiple Cylindrical Holes

In Korea, the Very High Temperature Gas-Cooled Reactor (VHTR) PMR200 is being developed in the Nuclear Hydrogen Development and Demonstration project. Its core consists of hexagonal prism-shaped graphite blocks for the fuel and reflector, and each hexagonal fuel block contains 108 cylindrical coolant holes and 210 fuel compacts. Because of these holes and fuels, the heat transfer in lateral directions in the fuel blocks becomes very complicated. Especially in accident situations when forced convection is lost, the majority of the afterheat flows in the radial direction by conduction across the large number of coolant holes. Moreover, radiation heat transfer is supposed to be added to the radial heat transfer modes owing to the high temperature of the VHTR core. Because of these complexities in radial heat transfer, reliable modeling for effective thermal conductivity (ETC) is required in order to analyze the reactor core thermal behavior using lumped-parameter codes, which are often used to evaluate the integrity of nuclear fuel embedded in the graphite block. In this study, the ETC model adopted in the GAMMA+ code was introduced, and the adequacy of the model was assessed by the commercial computational fluid dynamics (CFD) code CFX-13. The results of the CFD analysis were consistent with the ETC model in general even if a slight disagreement was shown for the case of high temperature. From these analyses, it could be concluded that the ETC model adopted in the GAMMA+ code is an adequate model for the analysis of the PMR200 reactor core. Moreover, it was found that the effect of fuel gap can cause an overprediction of the ETC if the fuel compact thermal conductivity is larger than the applicable range of the model.

Effect of Adding Horizontal Rings on the Thermal Behavior of Cylindrical Liquid Enclosure Exposed to High Heat Flux

Power generation by using concentrated solar thermal energy on liquid enclosures is one of the most promising renewable energy technologies. In this work, a developed liquid enclosure fitted with various number and configurations of horizontal metal rings have been analyzed, fabricated and tested. The influence of adding metal rings arrangement is investigated for its potential to enhance radial heat conduction to the center-line of the enclosure from the side-walls. Experiments were carried out for fluid in both static and dynamic modes of operation inside the enclosure that subjected to high heat flux.A developed two-dimensional CFD model to predict the transient flow and thermal fields within liquid enclosure subjected to heat flux has been developed and tested. The developed numerical model takes into consideration energy transport between the liquid inside enclosure and the solid material of the enclosure. The numerical simulations have been compared with experimental measurement. The computational code has been found in a good level of agreement with the experimental data except for liquid at the peak part of the enclosure. The results indicate that adding metal rings produce significant impact on the transient temperature difference inside enclosure during both static and dynamic modes. The six-ring model is found to be more effective for enhancing radial heat transfer than other three models that have been tested. The in-line arrangement is found to provide better thermal effect as compared to the staggered rings.Two new correlations for natural heat transfer inside liquid enclosures subjected to high heat flux have been formulated (one for no-ring model and the other for six-ring model). The natural Nusselt number is found to be around a constant value for Rayleigh number less than (5 x 108). The recommended use of metal rings inside liquid enclosures subjected to heat flux, and the predicted Nusselt number correlation, will add to local knowledge a significant mean to gain more heat in large scale concentrated solar power plants.

Turbulent convection experiment at high Rayleigh number to support CAP1400 IVR strategy

The characteristics of the heat transfer and the calculation of heat flux in metal layer are both the critical problems for in-vessel retention (IVR) strategy. Turbulent convection occurs in the metal layer when the Rayleigh number (Ra) becomes sufficient high. The Globe–Dropkin (G–D) correlation (Globe and Dropkin, 1959) and Chu–Churchill (C–C) correlation (Churchill and Chu, 1975) have been widely used to calculate the heat flux in the metal layer, where the valid range of the Ra is from 1.5×105 to 6.8×108 in G–D correlation and less than 1012 in C–C correlation. However, with the increase of reactor power, both the Rayleigh number and the rate of heat transfer below the bottom of metal layer of the molten pool will increase, and in this case the Rayleigh number even can reach 1011 for the China Advanced Passive Plant CAP1400. Accordingly, the G–D correlation is not suitable for the CAP1400. Therefore, our experiment purposes are to establish the appropriate correlation at high Ra for the CAP1400 and predict the axial and radial distribution of the heat transfer in the metal layer with the heat transfer behavior of metal layer experiment (HELM) facility.The experiments are divided into two parts. Each part concerns 39 runs and 47 experimental conditions. Its corresponding results are obtained at middle Prandtl number (Pr=7 for water) and the Nusselt number is found to be proportional to Ra0.315 in the range 3.93×108<Ra<3.57×1012. Furthermore, the experiment results can predict the relationship between axial and radial heat transfer well.

DETERMINATION OF THE EFFECTIVE RADIAL THERMAL DIFFUSIVITY FOR EVALUATING ENHANCED HEAT TRANSFER IN TUBES UNDER NON-NEWTONIAN LAMINAR FLOW

Enhanced heat transfer in tubes under laminar flow conditions can be found in coils or corrugated tubes or in the presence of high wall relative roughness, curves, pipe fittings or mechanical vibration. Modeling these cases can be complex because of the induced secondary flow. A modification of the Graetz problem for non-Newtonian power-law flow is proposed to take into account the augmented heat transfer by the introduction of an effective radial thermal diffusivity. The induced mixing was modeled as an increased radial heat transfer in a straight tube. Three experiments using a coiled tube and a tubular heat exchanger with high relative wall roughness are presented in order to show how this parameter can be obtained. Results were successfully correlated with Reynolds number. This approach can be useful for modeling laminar flow reactors (LFR) and tubular heat exchangers available in the chemical and food industries.

The Graetz–Nusselt problem extended to continuum flows with finite slip

AbstractGraetz and Nusselt studied heat transfer between a developed laminar fluid flow and a tube at constant wall temperature. Here, we extend the Graetz–Nusselt problem to dense fluid flows with partial wall slip. Its limits correspond to the classical problems for no-slip and no-shear flow. The amount of heat transfer is expressed by the local Nusselt number $\mathit{Nu}_{x}$, which is defined as the ratio of convective to conductive radial heat transfer. In the thermally developing regime, $\mathit{Nu}_{x}$ scales with the ratio of position $\tilde{x}=x/L$ to Graetz number $\mathit{Gz}$, i.e. $\mathit{Nu}_{x}\propto (\tilde{x}/\mathit{Gz})^{-{\it\beta}}$. Here, $L$ is the length of the heated or cooled tube section. The Graetz number $\mathit{Gz}$ corresponds to the ratio of axial advective to radial diffusive heat transport. In the case of no slip, the scaling exponent ${\it\beta}$ equals $1/3$. For no-shear flow, ${\it\beta}=1/2$. The results show that for partial slip, where the ratio of slip length $b$ to tube radius $R$ ranges from zero to infinity, ${\it\beta}$ transitions from $1/3$ to $1/2$ when $10^{-4}&lt;b/R&lt;10^{0}$. For partial slip, ${\it\beta}$ is a function of both position and slip length. The developed Nusselt number $\mathit{Nu}_{\infty }$ for $\tilde{x}/\mathit{Gz}&gt;0.1$ transitions from 3.66 to 5.78, the classical limits, when $10^{-2}&lt;b/R&lt;10^{2}$. A mathematical and physical explanation is provided for the distinct transition points for ${\it\beta}$ and $\mathit{Nu}_{\infty }$.

A critical review on heat transfer in trickle bed reactors

AbstractA critical review of the available information about heat transfer between a packed bed with cocurrent downflow of gas and liquid and an external medium was undertaken. Several aspects such as experimental set-ups and methods employed to study heat transfer in trickle bed reactors, models used to interpret experimental data, and literature correlations of heat transfer parameters are addressed. From the analysis of the available experimental information, a refined database has been built, which allows comparing the performance of the existing correlations for the parameters of the extensively employed two-dimensional pseudohomogeneous plug flow model (i.e., effective radial thermal conductivity and wall heat transfer coefficient). In addition, new correlations for effective thermal conductivity have been developed. Identification of gaps in the current knowledge and recommendations for future works are summarized.

Numerical Study on Local Flow Field and Temperature Field of Helical Baffles Heat Exchanger

Models of continuous helical baffles and quarter helical baffles heat exchangers are established. With large CFD analysis software FLUENT, the distribution characteristics of local flow field and temperature field of helical baffles heat exchangers are investigated through numerical simulation. And comprehensive performances of both heat exchangers are compared and studied with entransy dissipation. The results show:In the research of heat exchanger, the evaluation standard of entransy dissipation is consistent with that of comprehensive performances. When the flow of shell side is the same, the entransy dissipation value of continuous helical baffles heat exchanger is less than that of quarter helical baffles heat exchanger. The distribution characteristics of local flow field and temperature field of both heat exchangers present the same rules, in the central part of shell side, heat transfer coefficient of tubes is the highest. Along the radial direction, both helical flow and heat transfer coefficient of tubes first increase then decrease. Compared to continuous baffles, the discontinuity of baffles could enhance local heat transfer. Yet, when flow increases to an extent, the local heat transfer in the center will be weakened. The results provide theoretical basis for the improvement of structure forms of helical baffles.

The influence of the shuttle effect on the intensification of heat losses in a Stirling engine

The paper presents a methodology of calculating negative heat flows in the cylinder-piston group of theStirling engine. Some of the most important of them are the shuttle effect and the pumping losses. The introductorypart of the article describes the physical side of the phenomena under investigation. The main relationshipsrecommended by the researchers for the calculation of the shuttle effect and pumping losses are presented in thepaper. A mathematical model is developed for the purpose of calculating the heat losses mentioned. The model isbased on representing the phenomenon as quasistationary radial heat transfer by means of convection and radiation.A system of algebraic differential equations of heat exchange between single elements of arrays is presented.The system of the main equations is solved by a numerical method of integration (a variety of Euler method -the method of limiting overrelaxation). Algorithms of controlling the accuracy of the calculations performed areincorporated in the program of calculation. The algorithm is used for defining the level of shuttle conduction andpumping loss in the1R30/6 Stirling engine designed at Saint-Petersburg State Marine Technical University. Inaddition a methodology of finding the heat dissipation factor in the gap between the displacer and the cylinderwall was developed. The extent of influence of the engine design data on the phenomena under consideration isanalyzed. Rank diagrams are constructed that visualize the results obtained.

Study on Effective Radial Thermal Conductivity of Gas Flow through a Methanol Reactor

Abstract The heat conduction performance of the methanol synthesis reactor is significant for the development of large-scale methanol production. The present work has measured the temperature distribution in the fixed bed at air volumetric flow rate 2.4–7 m3 · h−1, inlet air temperature 160–200°C and heating tube temperature 210–270°C. The effective radial thermal conductivity and effective wall heat transfer coefficient were derived based on the steady-state measurements and the two-dimensional heat transfer model. A correlation was proposed based on the experimental data, which related well the Nusselt number and the effective radial thermal conductivity to the particle Reynolds number ranging from 59.2 to 175.8. The heat transfer model combined with the correlation was used to calculate the temperature profiles. A comparison with the predicated temperature and the measurements was illustrated and the results showed that the predication agreed very well with the experimental results. All the absolute values of the relative errors were less than 10%, and the model was verified by experiments. Comparing the correlations of both this work with previously published showed that there are considerable discrepancies among them due to different experimental conditions. The influence of the particle Reynolds number on the temperature distribution inside the bed was also discussed and it was shown that improving particle Reynolds number contributed to enhance heat transfer in the fixed bed.

Application of Computational Fluid Dynamics (CFD) for the Evaluation of Fluid Convective Radial Heat Transfer Parameters in Packed Beds

A model to simulate the behavior of multitubular packed-bed catalytic reactors was recently proposed [Asensio, D. A.; Zambon, M. T.; Mazza, G. D.; Barreto, G. F. Ind. Eng. Chem. Res. 2014, 53, 3587–3605]. In particular, the model introduces a heat transfer coefficient hwf that accounts for an unmixed fluid film on the wall and a coefficient hf between the fluid channels at a distance Dp/2 from the wall. Computational fluid dynamics simulations intended to evaluate these parameters are described. Four regular sphere arrays between parallel planes that provide different combinations of wall and core channel voidages (ε1 and εc) were employed. Reynolds and Prandtl numbers ranges were 100 < Rep < 2000 and 0.4 < Pr < 3.5. Calculated values of hwf and hf are well correlated with those of ε1, εc, Rep, and Pr. Results for ε1 and εc values typical of randomly packed beds of low ratio Dt/Dp show good agreement with carefully analyzed data from the literature.

An improved vibration technique for enhancing temperature uniformity and heat transfer in viscous fluid flow

Radial heat transfer in viscous pipe flow is controlled by thermal conduction which leads to a wide radial temperature distribution and slow heating of the core region of the flow. This is highly undesirable in many industrial processes as it results in a grossly uneven distribution of fluid heat treatment. The use of static in-line mixers to promote radial mixing and, thus, heat transfer and temperature uniformity, engenders large pressure drops and the devices are generally prohibited in processes where hygiene is paramount as they are difficult to keep clean. We recently reported a Computational Fluid Dynamics (CFD) study which showed that the superimposing of transverse mechanical oscillations on the steady flow of a viscous fluid in a pipe with an isothermal wall, results in a large enhancement in wall heat transfer, as well as a considerably more uniform radial temperature distribution accompanied by rapid heating of the inner region of the flow. Such a transverse vibration also causes the thermal boundary layer to grow more rapidly and, thus, the temperature profile to develop very rapidly in the axial direction. In this article, we report on an enhanced vibration technique which combines transverse oscillations with a step rotation of oscillation orientation. The technique produces much more improved effects compared to transverse vibration alone, and it also excels in comparison with the well-known Kenics helical static mixer.

Optimization of compact multitubular fixed-bed reactors for the methanol synthesis loaded with highly conductive structured catalysts

Abstract By computer simulation, we analyze the performances of a compact (2 meter-long) externally-cooled multitubular reactor for the methanol synthesis loaded with highly conductive structured catalysts, namely washcoated copper honeycomb monoliths and copper open-cell foams. Such a reactor is simulated as inserted in a synthesis loop including an ideal condenser, a recycle and a purge stream. Parametric analysis of the catalyst volumetric fraction points out that compact methanol structured reactors can be operated even with loadings as low as 0.30 m3 catalyst/m3 tube, but they would grant lower COx conversions per pass, resulting in higher recycle ratios. The excellent radial heat transfer performances of the structured reactors enable however the catalyst intrinsic activity and/or the coolant temperature to be properly optimized to compensate for the lower catalyst loads, eventually granting lower recycle ratios (i.e. keeping COx conversion per pass close to the equilibrium value) as well as limited hot-spot temperatures. Furthermore, reactor tubes with larger diameters can be adopted in compact conductive structured reactors loaded with limited catalyst volumetric fractions, thus allowing for reduction of investment costs. In particular, we show that, thanks also to the efficient radial heat transfer, the greater thermal loads generated in the configurations with larger tubes can be effectively managed to enhance the reactor performances.

Preparation and evaluation of a metallic foam catalyst for steam-CO2 reforming of methane in GTL-FPSO process

A metallic foam catalyst was used to improve the heat transfer of a reactor for the steam-CO2 reforming (SCR) of methane in the GTL-FPSO (gas to liquid-floating production storage and offloading) process. The metallic foam catalyst was prepared and examined by scanning electron microscopy, fall-off test and SCR reaction. The radial heat transfer was characterized in terms of the Nusselt number and was compared with the pellet catalyst to confirm the improvement in the heat transfer of the metallic foam catalyst. As a result of the fall-off test, the adhesion strength was highest at an Al2O3/AIP molar ratio of 5. The Nusselt number of the metallic foam catalyst was higher than that of the conventional pellet catalyst. Therefore, the reformer had a uniform temperature distribution along the catalyst-bed when the metallic foam catalyst was used.

Assessment of axial and radial heat transfer during immersion quenching of Inconel 600 probe

The time–temperature data at axial and radial locations were measured during immersion quenching of Inconel 600 probe in a mineral oil quench medium. The cooling of probe was not uniform during quenching. The variation of cooling rate along the axial direction was found to be higher than around the radial location. Inverse heat conduction problem (IHCP) was solved for estimating heat flux transients from the temperature data and thermo-physical properties of the Inconel probe. Single and multiple unknown heat fluxes were assigned on the metal/quenchant boundary. The error between the estimated and measured temperatures reduced significantly with increase in number of unknown surface heat flux components. The peak heat flux was about 50% lower for assignment of single unknown heat flux compared to multiple unknown heat fluxes at the metal/quenchant boundary. A plot of isotherms indicated gradual and uniform cooling of the quench probe when single heat flux boundary was used. With increase in the number of heat flux components, non-uniform and large temperature variations in the quench probe were observed. The present work outlines the importance of estimation of spatially dependent boundary heat flux transients during quench heat treatment.

Modeling of a pilot-scale fixed-bed reactor for iron-based Fischer–Tropsch synthesis: Two-dimensional approach for optimal tube diameter

The present work describes the development of a two-dimensional mathematical model of a pilot-scale fixed-bed reactor for Fe-based Fischer–Tropsch synthesis to evaluate the effect of tube diameter on temperature profile and catalyst performance. The entire chain lengths of the hydrocarbon products were lumped to form several representative components, and the apparent kinetic parameters for the reaction rates were estimated. The effectiveness of the developed model was corroborated by the comparison of temperature profiles, conversion, and selectivities between experimental and simulated results. The increase of tube diameter in the simulation showed that temperature increased in both the radial and the axial directions owing to the low radial heat transfer rate and the low heat transfer area, respectively. Finally, the specified diameter in the present study maintained the temperature below the threshold value and the methane selectivity below 10%.

A Lie Symmetry Classification of a Nonlinear Fin Equation in Cylindrical Coordinates

The nonlinear fin equation in cylindrical coordinates is considered. Assuming a radial variable heat transfer coefficient and temperature dependent thermal conductivity, a complete classification of these two functions is obtained via Lie symmetry analysis. Using these Lie symmetries, we carry out reduction of the fin equation and whenever possible exact solutions are obtained.